Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 6^(x−3)/4=√6

Key Concepts

Exponential Equations

Exponential equations are equations in which variables appear as exponents. To solve these equations, one common method is to express both sides of the equation with the same base. This allows us to equate the exponents directly, simplifying the process of finding the variable's value.

Properties of Exponents

The properties of exponents, such as the product of powers, power of a power, and quotient of powers, are essential for manipulating exponential expressions. For instance, when dividing like bases, we subtract the exponents. Understanding these properties helps in rewriting expressions to facilitate solving equations.

Square Roots and Exponents

The square root of a number can be expressed as an exponent of 1/2. For example, √6 can be rewritten as 6^(1/2). This concept is crucial when solving exponential equations, as it allows us to express both sides of the equation in terms of the same base, enabling the comparison of exponents.